Discussion
The number of microstates of distributing five quanta of energy among four distinguishable particles is :
Answer: A
The number of microstates is 56.
Distributing q identical quanta among N distinguishable particles is a stars-and-bars count: the number of ways is
\[ \begin{aligned} W &= \frac{(q + N - 1)!}{q!\,(N - 1)!} \\ &= \frac{8!}{5!\,3!} = \frac{8 \times 7 \times 6}{6} = 56 \end{aligned} \]
126 is what you get with N = 5 and q = 5 (9!/5!4!), mixing up the roles of particles and quanta, and 35 comes from 7!/4!3!, one too few in the numerator. 14 has no basis in the count.
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